Cutting length and bend deductions, explained properly

Take a bar dimensioned 1,500 mm along one leg and 800 mm along the other, with a 90° bend between them. How long is the bar you cut?

It is not 2,300 mm. It is slightly less — and the reason why is the single most misunderstood piece of arithmetic in bar bending schedule preparation.

Why the legs never add up

Dimensions on a reinforcement drawing are given to the outside intersection of the legs: the theoretical corner where the two straight lines would meet if the bar turned through a perfect, zero-radius angle.

Steel does not do that. A bar bent through 90° follows an arc around a mandrel of some finite radius. The arc is shorter than going out to the corner and back. That difference — between the path through the corner and the arc actually taken — is the bend deduction.

So:

cutting length = Σ dimensioned legs
               + Σ hook allowances
               − Σ bend deductions

Three terms. Miss the third and every bent bar on your schedule is cut long, which shows up as cutting waste. Apply it twice, or apply the wrong table, and bars come up short — which is far worse, because a short bar is scrap.

The deductions themselves

The deduction depends on the bend angle and the mandrel radius, and the mandrel radius is set by the bar diameter and the governing code. It is always expressed as a multiple of the bar diameter, d.

Indian practice, following IS 2502, uses these conventional values:

BS 8666:2020 works differently. Rather than a flat table by angle, it gives a cutting-length formula per shape code, with the deduction derived from the scheduling radius r set out in Table 2 of the standard. For bars up to 16 mm the deductions work out roughly half the IS values:

These are not interchangeable. Scheduling a BS 8666 job with IS deductions will cut every bent bar short. This is the most common failure mode when a team that normally works to IS picks up an export project, and it is expensive because it is systematic — it affects every bar, not one.

Hooks add, bends subtract

Hooks work in the opposite direction. A hook is extra steel beyond the dimensioned leg, so it is added:

The 135° hook is the one that matters most in Indian practice, because IS 13920 requires it for stirrups and ties in structures designed for ductility. If a schedule shows 90° hooks on seismic stirrups, that is a detailing error before it is an arithmetic one.

A worked example

A rectangular stirrup for a 300 × 450 beam, 25 mm cover, 8 mm bar, with two 135° seismic hooks.

Step 1 — the leg dimensions. Working to the centre line inside the cover:

short side  = 300 − (2 × 25) = 250 mm
long side   = 450 − (2 × 25) = 400 mm
total legs  = 2 × (250 + 400) = 1,300 mm

Step 2 — the hooks. Two 135° hooks at 10 d:

2 × 10 × 8 = 160 mm

Step 3 — the deductions. A closed rectangular stirrup with seismic hooks has three 90° corner bends and two 135° hook bends:

three 90°  : 3 × 2 d = 3 × 2 × 8 = 48 mm
two 135°   : 2 × 3 d = 2 × 3 × 8 = 48 mm
total              = 96 mm

Step 4 — the cutting length:

1,300 + 160 − 96 = 1,364 mm

You may have seen the shorthand 2(a + b) + 24d, which for this stirrup gives 1,492 mm. That rule of thumb bundles the hooks and deductions into one constant using a different set of conventions. It is close enough for a quick site check and not close enough for a schedule you are cutting 400 stirrups from — the difference here is 128 mm per stirrup, or about 51 m of 8 mm bar over the set.

Where this goes wrong in practice

Deductions ignored entirely. Every bent bar cut long. The loss is invisible because the bars still fit; it only surfaces as unexplained tonnage in the steel reconciliation.

The wrong code's table. Usually IS values on a BS job. Systematic short bars.

Mandrel radius assumed rather than looked up. The minimum scheduling radius increases with bar diameter. Using a small-bar radius on 32 mm bar understates the deduction, and on large diameters the error is substantial.

Shape code chosen to suit the spreadsheet. Picking a shape code because it is the one already in the template, rather than the one that matches the detail, quietly makes the whole calculation wrong regardless of how carefully it is then performed.

Get the arithmetic checked

The formulas are not difficult. Applying them consistently across a few thousand bar marks, to the right code, with the right radius, and keeping it correct through six drawing revisions — that is the actual work.

You can check your bar weights against the free rebar weight calculator, and the common BS 8666 shape codes with their cutting-length formulas are set out on our BBS preparation page.